The Canberra Times can reveal Labor backbenchers Alicia Payne and Luke Gosling will introduce their private member's bill next Monday, after it was rubber-stamped at a caucus meeting this afternoon.

Labor has agreed to grant a rare conscience vote because of the sensitivities around assisted dying, even though many of its members believe the bill is fundamentally about territory rights.

Ms Payne, who represents the seat of Canberra, is hopeful the bill can pass as soon as possible, although she is mindful of allowing time for all members to express their positions.

The legislation would repeal the so-called Andrews bill from 1997, which quashed the NT's world-first assisted dying regime and prevented both territories from making right-to-die laws in the future.

Labor's ACT and NT representatives have been pushing for a vote to be held as soon as possible in the new term, after Anthony Albanese promised to prioritise a debate if he won the May federal election.

Ms Payne, a Canberran who supports assisted dying, and Mr Gosling, a territorian who has strong reservations about it, were chosen to introduce the bill on behalf of the Labor's territory representatives after weeks of internal talks.

"I'm incredibly thankful for Prime Minister Albanese and our senior leadership for allowing this debate to happen in the first sitting," Ms Payne told The Canberra Times.

"It means so much to our constituents that they may soon have the same democratic rights as Australians living in the states."

The Payne-Gosling bill will be introduced in the House of Representatives, where it's understood the five ACT and NT representatives will each be offered time to speak.

It was understood that other speeches will be done in parliament's federation chamber, freeing up the lower house to deal with the government's packed legislative agenda.

There is no guarantee the bill will reach a vote in either house next week. A number of factors - including how many members wish to speak during the debate - will determine how quickly it proceeds.

After this sitting fortnight, parliament doesn't return until September 5.

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There is a widespread view that the bill will safely pass through the lower house, where Labor holds a slim majority and the Greens and so-called teal independents make up most of the crossbench.

The vote is expected to be tighter in the Senate, with the outcome likely to hinge on the number of opponents on the Labor side and the number of supporters from the Coalition.

Coalition senators Simon Birmingham and Andrew Bragg have already publicly declared their support for repealing the Andrews bill.

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